Properties

Label 5148.2
Level 5148
Weight 2
Dimension 323872
Nonzero newspaces 120
Sturm bound 2903040

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Defining parameters

Level: \( N \) = \( 5148 = 2^{2} \cdot 3^{2} \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 120 \)
Sturm bound: \(2903040\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5148))\).

Total New Old
Modular forms 735360 327432 407928
Cusp forms 716161 323872 392289
Eisenstein series 19199 3560 15639

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5148))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
5148.2.a \(\chi_{5148}(1, \cdot)\) 5148.2.a.a 1 1
5148.2.a.b 1
5148.2.a.c 1
5148.2.a.d 1
5148.2.a.e 1
5148.2.a.f 1
5148.2.a.g 2
5148.2.a.h 2
5148.2.a.i 2
5148.2.a.j 2
5148.2.a.k 2
5148.2.a.l 3
5148.2.a.m 3
5148.2.a.n 3
5148.2.a.o 3
5148.2.a.p 4
5148.2.a.q 4
5148.2.a.r 4
5148.2.a.s 5
5148.2.a.t 5
5148.2.b \(\chi_{5148}(2287, \cdot)\) n/a 416 1
5148.2.c \(\chi_{5148}(287, \cdot)\) n/a 240 1
5148.2.d \(\chi_{5148}(989, \cdot)\) 5148.2.d.a 48 1
5148.2.e \(\chi_{5148}(1585, \cdot)\) 5148.2.e.a 2 1
5148.2.e.b 4
5148.2.e.c 8
5148.2.e.d 10
5148.2.e.e 10
5148.2.e.f 24
5148.2.n \(\chi_{5148}(703, \cdot)\) n/a 360 1
5148.2.o \(\chi_{5148}(1871, \cdot)\) n/a 280 1
5148.2.p \(\chi_{5148}(2573, \cdot)\) 5148.2.p.a 56 1
5148.2.q \(\chi_{5148}(133, \cdot)\) n/a 280 2
5148.2.r \(\chi_{5148}(1717, \cdot)\) n/a 240 2
5148.2.s \(\chi_{5148}(529, \cdot)\) n/a 280 2
5148.2.t \(\chi_{5148}(3565, \cdot)\) n/a 116 2
5148.2.u \(\chi_{5148}(395, \cdot)\) n/a 672 2
5148.2.w \(\chi_{5148}(2179, \cdot)\) n/a 700 2
5148.2.y \(\chi_{5148}(109, \cdot)\) n/a 140 2
5148.2.ba \(\chi_{5148}(2465, \cdot)\) 5148.2.ba.a 44 2
5148.2.ba.b 44
5148.2.bc \(\chi_{5148}(1873, \cdot)\) n/a 240 4
5148.2.bh \(\chi_{5148}(2773, \cdot)\) n/a 120 2
5148.2.bi \(\chi_{5148}(4553, \cdot)\) n/a 112 2
5148.2.bj \(\chi_{5148}(3851, \cdot)\) n/a 560 2
5148.2.bk \(\chi_{5148}(3475, \cdot)\) n/a 832 2
5148.2.bp \(\chi_{5148}(155, \cdot)\) n/a 1680 2
5148.2.bq \(\chi_{5148}(2419, \cdot)\) n/a 1728 2
5148.2.br \(\chi_{5148}(329, \cdot)\) n/a 336 2
5148.2.bs \(\chi_{5148}(1739, \cdot)\) n/a 1680 2
5148.2.bt \(\chi_{5148}(835, \cdot)\) n/a 2000 2
5148.2.bu \(\chi_{5148}(857, \cdot)\) n/a 336 2
5148.2.cd \(\chi_{5148}(725, \cdot)\) n/a 336 2
5148.2.ce \(\chi_{5148}(1231, \cdot)\) n/a 2000 2
5148.2.cf \(\chi_{5148}(23, \cdot)\) n/a 1680 2
5148.2.cg \(\chi_{5148}(1121, \cdot)\) n/a 336 2
5148.2.ch \(\chi_{5148}(1453, \cdot)\) n/a 280 2
5148.2.ci \(\chi_{5148}(43, \cdot)\) n/a 2000 2
5148.2.cj \(\chi_{5148}(419, \cdot)\) n/a 1680 2
5148.2.cs \(\chi_{5148}(2003, \cdot)\) n/a 1440 2
5148.2.ct \(\chi_{5148}(571, \cdot)\) n/a 2000 2
5148.2.cu \(\chi_{5148}(1057, \cdot)\) n/a 280 2
5148.2.cv \(\chi_{5148}(1517, \cdot)\) n/a 336 2
5148.2.cw \(\chi_{5148}(815, \cdot)\) n/a 1680 2
5148.2.cx \(\chi_{5148}(439, \cdot)\) n/a 2000 2
5148.2.cy \(\chi_{5148}(3301, \cdot)\) n/a 280 2
5148.2.cz \(\chi_{5148}(2705, \cdot)\) n/a 288 2
5148.2.de \(\chi_{5148}(3761, \cdot)\) n/a 112 2
5148.2.df \(\chi_{5148}(3059, \cdot)\) n/a 560 2
5148.2.dg \(\chi_{5148}(4267, \cdot)\) n/a 832 2
5148.2.dl \(\chi_{5148}(233, \cdot)\) n/a 224 4
5148.2.dm \(\chi_{5148}(2107, \cdot)\) n/a 1440 4
5148.2.dn \(\chi_{5148}(467, \cdot)\) n/a 1344 4
5148.2.dw \(\chi_{5148}(2393, \cdot)\) n/a 192 4
5148.2.dx \(\chi_{5148}(181, \cdot)\) n/a 280 4
5148.2.dy \(\chi_{5148}(415, \cdot)\) n/a 1664 4
5148.2.dz \(\chi_{5148}(2159, \cdot)\) n/a 1152 4
5148.2.ea \(\chi_{5148}(463, \cdot)\) n/a 3360 4
5148.2.ec \(\chi_{5148}(1451, \cdot)\) n/a 4000 4
5148.2.ef \(\chi_{5148}(241, \cdot)\) n/a 672 4
5148.2.eh \(\chi_{5148}(89, \cdot)\) n/a 192 4
5148.2.ej \(\chi_{5148}(353, \cdot)\) n/a 560 4
5148.2.el \(\chi_{5148}(505, \cdot)\) n/a 280 4
5148.2.en \(\chi_{5148}(1957, \cdot)\) n/a 672 4
5148.2.ep \(\chi_{5148}(1541, \cdot)\) n/a 560 4
5148.2.er \(\chi_{5148}(2243, \cdot)\) n/a 4000 4
5148.2.et \(\chi_{5148}(1783, \cdot)\) n/a 1400 4
5148.2.ev \(\chi_{5148}(1255, \cdot)\) n/a 3360 4
5148.2.ex \(\chi_{5148}(791, \cdot)\) n/a 1344 4
5148.2.ez \(\chi_{5148}(527, \cdot)\) n/a 4000 4
5148.2.fb \(\chi_{5148}(67, \cdot)\) n/a 3360 4
5148.2.fc \(\chi_{5148}(749, \cdot)\) n/a 560 4
5148.2.fe \(\chi_{5148}(1165, \cdot)\) n/a 672 4
5148.2.fg \(\chi_{5148}(289, \cdot)\) n/a 560 8
5148.2.fh \(\chi_{5148}(445, \cdot)\) n/a 1344 8
5148.2.fi \(\chi_{5148}(157, \cdot)\) n/a 1152 8
5148.2.fj \(\chi_{5148}(841, \cdot)\) n/a 1344 8
5148.2.fl \(\chi_{5148}(73, \cdot)\) n/a 560 8
5148.2.fn \(\chi_{5148}(125, \cdot)\) n/a 448 8
5148.2.fp \(\chi_{5148}(359, \cdot)\) n/a 2688 8
5148.2.fr \(\chi_{5148}(775, \cdot)\) n/a 3328 8
5148.2.fw \(\chi_{5148}(179, \cdot)\) n/a 2688 8
5148.2.fx \(\chi_{5148}(523, \cdot)\) n/a 3328 8
5148.2.fy \(\chi_{5148}(17, \cdot)\) n/a 448 8
5148.2.gd \(\chi_{5148}(25, \cdot)\) n/a 1344 8
5148.2.ge \(\chi_{5148}(365, \cdot)\) n/a 1152 8
5148.2.gf \(\chi_{5148}(731, \cdot)\) n/a 8000 8
5148.2.gg \(\chi_{5148}(1843, \cdot)\) n/a 8000 8
5148.2.gh \(\chi_{5148}(1609, \cdot)\) n/a 1344 8
5148.2.gi \(\chi_{5148}(29, \cdot)\) n/a 1344 8
5148.2.gj \(\chi_{5148}(443, \cdot)\) n/a 6912 8
5148.2.gk \(\chi_{5148}(259, \cdot)\) n/a 8000 8
5148.2.gt \(\chi_{5148}(283, \cdot)\) n/a 8000 8
5148.2.gu \(\chi_{5148}(191, \cdot)\) n/a 8000 8
5148.2.gv \(\chi_{5148}(425, \cdot)\) n/a 1344 8
5148.2.gw \(\chi_{5148}(49, \cdot)\) n/a 1344 8
5148.2.gx \(\chi_{5148}(211, \cdot)\) n/a 8000 8
5148.2.gy \(\chi_{5148}(1895, \cdot)\) n/a 8000 8
5148.2.gz \(\chi_{5148}(173, \cdot)\) n/a 1344 8
5148.2.hi \(\chi_{5148}(545, \cdot)\) n/a 1344 8
5148.2.hj \(\chi_{5148}(335, \cdot)\) n/a 8000 8
5148.2.hk \(\chi_{5148}(139, \cdot)\) n/a 8000 8
5148.2.hl \(\chi_{5148}(101, \cdot)\) n/a 1344 8
5148.2.hm \(\chi_{5148}(311, \cdot)\) n/a 8000 8
5148.2.hn \(\chi_{5148}(79, \cdot)\) n/a 6912 8
5148.2.hs \(\chi_{5148}(575, \cdot)\) n/a 2688 8
5148.2.ht \(\chi_{5148}(127, \cdot)\) n/a 3328 8
5148.2.hu \(\chi_{5148}(361, \cdot)\) n/a 560 8
5148.2.hv \(\chi_{5148}(809, \cdot)\) n/a 448 8
5148.2.ib \(\chi_{5148}(5, \cdot)\) n/a 2688 16
5148.2.id \(\chi_{5148}(733, \cdot)\) n/a 2688 16
5148.2.ie \(\chi_{5148}(167, \cdot)\) n/a 16000 16
5148.2.ig \(\chi_{5148}(115, \cdot)\) n/a 16000 16
5148.2.ii \(\chi_{5148}(163, \cdot)\) n/a 6656 16
5148.2.ik \(\chi_{5148}(479, \cdot)\) n/a 16000 16
5148.2.im \(\chi_{5148}(215, \cdot)\) n/a 5376 16
5148.2.io \(\chi_{5148}(427, \cdot)\) n/a 16000 16
5148.2.iq \(\chi_{5148}(193, \cdot)\) n/a 2688 16
5148.2.is \(\chi_{5148}(245, \cdot)\) n/a 2688 16
5148.2.iu \(\chi_{5148}(449, \cdot)\) n/a 896 16
5148.2.iw \(\chi_{5148}(85, \cdot)\) n/a 2688 16
5148.2.iy \(\chi_{5148}(145, \cdot)\) n/a 1120 16
5148.2.ja \(\chi_{5148}(137, \cdot)\) n/a 2688 16
5148.2.jd \(\chi_{5148}(31, \cdot)\) n/a 16000 16
5148.2.jf \(\chi_{5148}(83, \cdot)\) n/a 16000 16

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5148))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5148)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(99))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(132))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(198))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(286))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(396))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(429))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(468))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(572))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(858))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1287))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1716))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2574))\)\(^{\oplus 2}\)